Two times the difference between a number and eight

Question

Two times the difference between a number and eight is less than or equal to six times the sum of the number and four. Find the smallest number that will satisfy the inequality

Answer 1

Hi Amanda.

 

Start by making x stand for the number.

 

Then translate the sentence word for word into an equation:

Two times   the difference between a number & 8      is less than or equal to      6 times     the sum of the number & 4

2                                  (x - 8)                                           <=                           6                           (x + 4)

 

And solve: 2(x - 8) <= 6(x + 4)

                2x - 16 <= 6x + 24

                     -40 <= 4x

                     -10 <= x

                       x >= -10

 

Since x can be greater than or equal to -10, -10 would be the smallest number that would satisfy the inequality.

 

Check:

2(-10 - 8) <= 6(-10 + 4)

2(-18) <= 6(-6)

-36 <= -36 so -10 is the correct number.

 

Then check to see if the inequality symbol is facing the correct way. Choose a number that should work if it is. 0 is >+ -10 so try 0 in the original equation.

2(0 - 8) <= 6(0 + 4)

2(-8) <= 6(4)

-16 <= 24 yes, that is true, so our answer should be correct.